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J. Chem. Inf. Comput. Sci. 2001, 41, 692-701
Quantitative Structure-Property Relationships (QSPRs) for the Estimation of Vapor Pressure: A Hierarchical Approach Using Mathematical Structural Descriptors Subhash C. Basak* and Denise Mills Natural Resources Research Institute, University of MinnesotasDuluth, 5013 Miller Trunk Highway, Duluth, Minnesota 55811 Received December 18, 2000
A set of 379 molecular descriptors was calculated for use in hierarchical quantitative structure-property relationship (QSPR) modeling of vapor pressure for a structurally diverse database consisting of 469 chemicals. The hierarchical approach utilizes topostructural, topochemical, geometrical, and quantum chemical descriptors in a stepwise fashion to develop QSPR models. In this way, the relative roles of the various levels of descriptors can be examined. The results show that the easily calculated topological descriptors explain the majority of the variance and that the addition of geometrical and quantum chemical descriptors does not result in a significantly improved model. 1. INTRODUCTION
One of the major interests in environmental sciences and ecotoxicology is the assessment of fate, transport, and distribution of chemicals. The distribution of chemicals among water, air, and soil is governed primarily by some key physicochemical properties such as vapor pressure, water solubility, air-water partition coefficient, soil sorption, Henry’s law constant, etc.1-3 Vapor pressure (VP) plays a critical role in the transport, fate, and distribution of pollutants in the ecosystem and hence determines the acceptability of chemical substances and processes that produce them. For environmental pollutants, a knowledge of their VP gives an idea about their distribution between the atmosphere and the soil. In the case of a toxic chemical spill, its VP can be used to estimate the rate at which the chemical evaporates to the atmosphere. VP data are also used in the estimation of liquid viscosity, enthalpy of vaporization, air-water partition coefficient, and flash points.4 The vapor pressure of the ever increasing number of chemicals cannot be determined in the laboratory due to the lack of resources and facilities. Another problem area is the VP of low-volatility chemicals where there are analytical difficulties in their determination. Estimation of vapor pressure can be accomplished utilizing models where one uses other physicochemical properties. For example, Mackay et al.5 developed a VP model using boiling point (Tb) and melting point (Tm), and Banerjee et al.6 developed a model using molar volume (V), polarizability/dipolarity (π*), and melting point (Tm). In such models, physicochemical properties are the independent variables which, in turn, either have to be determined in the laboratory (which is again costly and time-consuming) or derived from various estimation methods. Quantitative structure-property relationship (QSPR) models provide a viable alternative by estimating VP using parameters which can be calculated directly from molecular * Corresponding author phone: (218)720-4230; fax: (218)720-4328; e-mail:
[email protected].
structure of chemicals without any input of experimental data.7-11 Research in many scientific fields including toxicology and drug design as well as regulation of chemicals have become increasingly dependent on predictive quantitative structure-property/activity relationships (QSPRs/QSARs). While many studies have been carried out using property values rather than structural information in order to develop predictive models, the limitations of this approach due to a profound lack of experimental data has become painfully obvious. For example, there is no property data at all available for approximately 50% of the roughly 80 000 chemicals listed currently in the Toxic Substances Control Act (TSCA) Inventory.12 With the advent of combinatorial chemistry, where it is possible to quickly create libraries containing thousands of real or hypothetical chemicals, the number of chemical structures without accompanying property data is increasing dramatically. The cost involved in the laboratory testing of such large numbers of chemicals is prohibitive. Theoretical molecular descriptors, on the other hand, can be calculated algorithmically for any chemicals real or hypothetical. These descriptors can be calculated for large numbers of chemicals at a minimal cost. We have recently formulated a hierarchical approach where calculated parameters of increasing complexity, viz., topostructural, topochemical, geometrical, and quantum chemical parameters, have been used in the formulation of QSARs/QSPRs for the prediction of biomedicinal, physicochemical, and toxicological properties.7,13-20 In an earlier paper, Basak et al.7 used a set of calculated molecular descriptors to estimate VP of a set of 476 chemicals with good results. In this paper, we have formulated QSPR models on a set of 469 compounds with an expanded set of calculated parameters which led to a significant improvement in the predictive power of the model. 2. MATERIALS AND METHODS
2.1. Database. The set of 469 chemicals used in this study is a subset of the 476 chemicals used in the previous study
10.1021/ci000165r CCC: $20.00 © 2001 American Chemical Society Published on Web 04/11/2001
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Table 1. Chemical Class Composition of the Vapor Pressure Data Set compd classification
no. of compds
pure
substituted
total data set hydrocarbons non-hydrocarbons nitro compounds amines nitriles ketones halogens anhydrides esters carboxylic acids alcohols sulfides thiols imines epoxides aromatic compoundsa fused-ring compoundsb
469 253 216 4 20 5 7 97 1 18 2 10 38 4 2 1 15 1
3 17 4 7 92 1 16 2 6 37 4 2 1 10 1
1 3 1 0 5 0 2 0 4 1 0 0 0 4 0
a The 15 aromatic compounds are a mixture of 11 aromatic hydrocarbons and four aromatic halides. b The only fused-ring compound was a polycyclic aromatic hydrocarbon.
by Basak et al.7 which was obtained from the Assessment Tools for the Evaluation of Risk (ASTER) database21 and represents a subset of the Toxic Substances Control Act (TSCA) Inventory12 for which vapor pressure (pvap) was measured at 25 °C with a pressure range of approximately 3-10 000 mmHg. Of the 476 chemicals in the original data set, seven were two-atom compounds and thus not included in the present study due to the fact that the triplet indices, which are described in the following section, cannot be calculated for two-atom compounds. The molecular weights of the compounds in this data set range from 40 to 338, and the chemical diversity is described in Table 1. 2.2. Calculation of Molecular Descriptors. The majority of the topological descriptors were calculated using software developed by Basak et al., including POLLY 2.322 and H-Bond.23 The topological descriptors include Wiener number,24 molecular connectivity indices developed by Randic´25 and Kier and Hall,26 frequency of path lengths of varying size,26 information theoretic indices defined on distance matrices of graphs using the methods of Bonchev and Trinajstic´,27 Roy et al.,28 Basak et al.29-32 as well as those of Raychaudhury et al.,33 parameters defined on the neighborhood complexity of vertices in hydrogen-filled molecular graphs,29-33 a simple hydrogen bonding parameter,23 and Balaban’s J indices34 as well as the triplet indices.35,36 The triplets result from a matrix, main diagonal column vector, and free term column vector which are converted into a system of linear equations. The notation used to represent the vectors and matrices is as follows: A ) adjacency matrix, V ) vertex degree, S ) distance sum, N ) total number of vertices in the graph, Z ) atomic number, D ) distance matrix, and 1 ) unity matrix. After the system of N linear equations is solved, the local vertex invariants, xi, are assembled into a triplet descriptor based on one of the following operations: (1) summation, ∑ixi; (2) summation of squares, ∑ixi2; (3) summation of square roots, ∑ixi1/2; (4) sum of inverse square root of cross-product over edges ij, ∑ij(xixj)-1/2; and (5) product, N(∑ixi)1/N. Additional topological descriptors, including an extended set of molecular connectivity indices, electrotopological state
descriptors, general polarity descriptors, and hydrogen bonding descriptors, were calculated by Molconn-Z 3.50.37 A total number of 363 topological descriptors was calculated for use in the current study. Ten geometrical descriptors were used, including six kappa shape indices which were also calculated by Molconn-Z. van der Waals volume, VW, was calculated using Sybyl 6.2.38 In addition, two variants of the 3-D Wiener number, 3DW and 3DW , based on the hydrogen-suppressed and hydrogen-filled H geometric distance matrices, respectively, were also calculated by Sybyl using a SPL (Sybyl Programming Language) program developed by our group. The six quantum chemical descriptors included in the study, namely, EHOMO, EHOMO-1, ELUMO, ELUMO+1, ∆Hf, and µ, were calculated for the AM1 semiempirical Hamiltonian using MOPAC 6.0 in the Sybl interface.39 A complete list of the 379 parameters calculated for use in the current study, including brief descriptions, is provided in Table 2. 2.3. Hierarchical QSPR. QSPR modeling was performed in a hierarchical fashion, utilizing descriptor classes of increasing complexity. The set of topological descriptors was partitioned into two distinct subsets: topostructural (TS) and topochemical (TC). Topostructural descriptors encode information about the adjacency and distances of atoms in molecular structures irrespective of the chemical nature of the atoms, while topochemical descriptors encode information regarding the connectivity as well as specific chemical properties of the atoms making up the molecule. The topostructural descriptors are at the lowest level of the hierarchy, followed by the topochemical, the geometrical (3D), and finally the quantum chemical (QC). Initially, a model is developed utilizing only TS descriptors, after which TC descriptors are added to the parameters in the TS model, and the regression analysis is repeated to obtain a TS + TC model. This process is repeated, resulting in a TS + TC + 3D model and finally a TS + TC + 3D + QC model. 2.4. Data Reduction and Statistical Analysis. Prior to analysis, all calculated descriptors with nonnegative values were transformed by ln(descriptor value + 1) due to the fact that their scales differed by several orders of magnitude, and some had a value of 0. A constant was added to the descriptors with negative values, such that their sum was greater than 0, before taking the natural logarithm. Any descriptor with a value of 0 for all compounds was removed from the pool and not used in subsequent analyses. Perfectly correlated descriptors, i.e. those having a correlation coefficient of 1.0, were identified using the CORR procedure40 of the SAS statistical software package. In each case, only one of the perfectly correlated descriptors was retained and used in subsequent analyses. The number of descriptors remaining (268) was still too large with respect to the number of observations (469) and had to be decreased in order to reduce the probability of chance correlations. To this end, the VARCLUS40 procedure of the SAS software package was used. In this procedure, each descriptor is assigned to one, and only one, cluster. From each cluster, we selected the one descriptor most highly correlated and all descriptors poorly correlated (R 2 < 0.7) with that cluster. In the event that there were two most highly correlated descriptors for a given cluster, the descriptor which was least correlated with the next closest cluster was selected.
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Table 2. Symbols, Definitions, and Classification of Molecular Descriptors IWD hIWD W ID HV HD IC M1 M2 h χ hχ C h χPC hχ Ch Ph J nrings ncirc DN2Sy DN21y AS1y DS1y ASNy DSNy DN2Ny ANSy AN1y ANNy ASVy DSVy ANVy O Oorb IORB ICr SICr CICr hχb hχb C hχb Ch h b χ PC hχv h v χC hχv Ch h v χ PC JB JX JY HB1 AZVy AZSy ASZy AZNy ANZy DSZy DN2Zy nvx nelem fw hχv hχv Ch si totop sumI sumdelI tets2 phia Idcbar IdC Wp Pf Wt
Topostructural (TS) information index for the magnitudes of distances between all possible pairs of vertices of a graph mean information index for the magnitude of distance Wiener index ) half-sum of the off-diagonal elements of the distance matrix of a graph degree complexity graph vertex complexity graph distance complexity information content of the distance matrix partitioned by frequency of occurrences of distance h a Zagreb group parameter ) sum of square of degree over all vertices a Zagreb group parameter ) sum of cross-product of degrees over all neighboring (connected) vertices path connectivity index of order h ) 0-10 cluster connectivity index of order h ) 3-6 path-cluster connectivity index of order h ) 4-6 chain connectivity index of order h ) 3-10 number of paths of length h ) 0-10 Balaban’s J index based on topological distance number of rings in a graph number of circuits in a graph triplet index from distance matrix, square of graph order, and distance sum; operation y ) 1-5 triplet index from distance matrix, square of graph order, and number 1; operation y ) 1-5 triplet index from adjacency matrix, distance sum, and number 1; operation y ) 1-5 triplet index from distance matrix, distance sum, and number 1; operation y ) 1-5 triplet index from adjacency matrix, distance sum, and graph order; operation y ) 1-5 triplet index from distance matrix, distance sum, and graph order; operation y ) 1-5 triplet index from distance matrix, square of graph order, and graph order; operation y ) 1-5 triplet index from adjacency matrix, graph order, and distance sum; operation y ) 1-5 triplet index from adjacency matrix, graph order, and number 1; operation y ) 1-5 triplet index from adjacency matrix, graph order, and graph order again; operation y ) 1-5 triplet index from adjacency matrix, distance sum, and vertex degree; operation y ) 1-5 triplet index from distance matrix, distance sum, and vertex degree; operation y ) 1-5 triplet index from adjacency matrix, graph order, and vertex degree; operation y ) 1-5 Topochemical (TC) order of neighborhood when ICr reaches its maximum value for the hydrogen-filled graph order of neighborhood when ICr reaches its maximum value for the hydrogen-suppressed graph information content or complexity of the hydrogen-suppressed graph at its maximum neighborhood of vertices mean information content or complexity of a graph based on the rth (r ) 0-6) order neighborhood of vertices in a hydrogen-filled graph structural information content for rth (r ) 0-6) order neighborhood of vertices in a hydrogen-filled graph complementary information content for rth (r ) 0-6) order neighborhood of vertices in a hydrogen-filled graph bond path connectivity index of order h ) 0-6 bond cluster connectivity index of order h ) 3-6 bond chain connectivity index of order h ) 3-6 bond path-cluster connectivity index of order h ) 4-6 valence path connectivity index of order h ) 0-6 valence cluster connectivity index of order h ) 3-6 valence chain connectivity index of order h ) 3-6 valence path-cluster connectivity index of order h ) 4-6 Balaban’s J index based on bond types Balaban’s J index based on relative electronegativities Balaban’s J index based on relative covalent radii hydrogen bonding parameter triplet index from adjacency matrix, atomic number, and vertex degree; operation y ) 1-5 triplet index from adjacency matrix, atomic number, and distance sum; operation y ) 1-5 triplet index from adjacency matrix, distance sum, and atomic number; operation y ) 1-5 triplet index from adjacency matrix, atomic number, and graph order; operation y ) 1-5 triplet index from adjacency matrix, graph order, and atomic number; operation y ) 1-5 triplet index from distance matrix, distance sum, and atomic number; operation y ) 1-5 triplet index from distance matrix, square of graph order, and atomic number; operation y ) 1-5 number of non-hydrogen atoms in a molecule number of elements in a molecule molecular weight valence path connectivity index of order h ) 7-10 valence chain connectivity index of order h ) 7-10 Shannon information index total topological index t sum of the intrinsic state values I sum of delta-I values total topological state index based on electrotopological state indices flexibility index (kp1* kp2/nvx) Bonchev-Trinajstic´ information index Bonchev-Trinajstic´ information index Wienerp Plattf total Wiener number
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Table 2 (Continued) knotp knotpv nclass numHBd numHBa SHCsats SHCsatu SHvin SHtvin SHavin SHarom SHHBd SHwHBd SHHBa Qv NHBinty SHBinty
Topochemical (TC) difference of chi-cluster-3 and path/cluster-4 valence difference of chi-cluster-3 and path/cluster-4 number of classes of topologically (symmetry) equivalent graph vertices number of hydrogen bond donors number of hydrogen bond acceptors E-state of C sp3 bonded to other saturated C atoms E-state of C sp3 bonded to unsaturated C atoms E-state of C atoms in the vinyl group, dCHE-state of C atoms in the terminal vinyl group, dCH2 E-state of C atoms in the vinyl group, dCH-, bonded to an aromatic C E-state of C sp2 which are part of an aromatic system hydrogen bond donor index, sum of hydrogen E-state values for -OH, dNH, -NH2, -NH-, -SH, and #CH weak hydrogen bond donor index, sum of C-H hydrogen E-state values for hydrogen atoms on a C to which a F and/or Cl are also bonded hydrogen bond acceptor index, sum of the E-state values for -OH, dNH, -NH2, -NH-, >N-, -O-, -S-, along with -F and -Cl general polarity descriptor count of potential internal hydrogen bonders (y ) 2-10) E-state descriptors of potential internal hydrogen bond strength (y )2-10) electrotopological state index values for atoms types: SHsOH, SHdNH, SHsSH, SHsNH2, SHssNH, SHtCH, Shother, SHCHnX, Hmax Gmax, Hmin, Gmin, Hmaxpos, Hminneg, SsLi, SssBe, Sssss, Bem, SssBH,SsssB, SssssBm, SsCH3, SdCH2, SssCH2, StCH, SdsCH, SaaCH, SsssCH, SddC, StsC, SdssC, SaasC, SaaaC, SssssC, SsNH3p, SsNH2, SssNH2p, SdNH, SssNH, SaaNH, StN, SsssNHp, SdsN, SaaN, SsssN, SddsN, SaasN, SssssNp, SsOH, SdO, SssO, SaaO, SsF, SsSiH3, SssSiH2, SsssSiH, SssssSi, SsPH2, SssPH, SsssP, SdsssP, SsssssP, SsSH, SdS, SssS, SaaS, SdssS, SddssS, SssssssS, SsCl, SsGeH3, SssGeH2, SsssGeH, SssssGe, SsAsH2, SssAsH, SsssAs, SdsssAs, SsssssAs, SsSeH, SdSe, SssSe, SaaSe, SdssSe, SddssSe, SsBr, SsSnH3, SssSnH2, SsssSnH, SssssSn, SsI, SsPbH3, SssPbH2, SsssPbH, SssssPb
kp0 kp1-kp3 ka1-ka3 VW 3D W 3DW H
Geometrical (3D) kappa zero kappa simple indices kappa alpha indices van der Waals volume 3D Wiener number based on the hydrogen-suppressed geometric distance matrix 3D Wiener number based on the hydrogen-filled geometric distance matrix
EHOMO EHOMO-1 ELUMO ELUMO+1 ∆Hf µ
Quantum Chemical (QC) energy of the highest occupied molecular orbital energy of the second highest occupied molecular energy of the lowest unoccupied molecular orbital energy of the second lowest unoccupied molecular orbital heat of formation dipole moment
Table 3. Descriptors Used in Hierarchical Model Development (Eqs 1-3) and the Type I Nonhierarchical Model (Eq 4) for the Set of 469 Diverse Chemicalsa
a
descriptor class
descriptors
TS TC
6χ 7χ 8χ 4χ 6χ 4χ 6χ 3χ 5χ 8χ P P P J W IC ASN DN2N DN2S ASV DSV ANV ANV NRINGS C C PC PC Ch Ch Ch 6 7 9 2 5 4 1 1 2 5 0χv 3χv 4χv 8χv 5χb 3χv 6 v 3 b 5 b 5 b Y Ch χ Ch χ C χ C χ PC J Oorb IC1 IC5 CIC1 CIC4 SIC0 ASZ2 AZV1 AZV4 AZN4 TOTOP TETS2
3D QC
IDCBAR SHOTHER NELEM HMIN SSCH3 SSBR SUMI PHIA HMAX SHCHNX SSCL SSSSN SSNH2 SAACH SAAS SSSNH HB1 STCH STSC SSF SHHBA SHVIN SHTVIN SHSSH SSSS SDDC SDSN SDS SHBINT3 SDO SSSO NUMHBD NHBINT2 STN SHCSATS SSI SAAO SHSOH VW 3DW 3DWH KP0-KP3 KA1-KA3 EHOMO EHOMO-1 ELUMO ELUMO+1 ∆Hf µ
TS and TC descriptors were clustered independently. All 3D and QC descriptors were used.
The VARCLUS40 procedure was used in two types of variable selection methodologies: (1) Variable clustering was performed independently on each of the TS and TC classes. The TS and TC descriptors selected by variable clustering, the 10 3D descriptors, and the six QC descriptors (a total of 101 descriptors) were used in regression analysis. A list of these descriptors can be found in Table 3. (2) The entire pool of descriptors (268), regardless of hierarchical class, was clustered together, and the selected descriptors (68) were used in regression analysis. A list of these descriptors can be found in Table 4.
For the sake of brevity, the actual clustering results, which indicate cluster membership and correlation coefficients for each descriptor with its own cluster and with the next closest cluster, have not been included in this paper for all three of the clustering procedures which were performed in this study (TS, TC, and all descriptors). However, the clustering results for methodology (2) above, in which all descriptors were clustered together, is available in Table 5. The descriptors selected via methodology (1) above were used both in the hierarchical model development and in the development of one type of nonhierarchical model (Type I). The descriptors selected via methodology (2) above were
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Table 4. Descriptors Used in Type II Nonhierarchical Model Development (Eq 5) for the Set of 469 Diverse Chemicals, Selected by Variable Clustering of the Entire Pool of Descriptors descriptor class TS TC 3D QC
descriptors 7χ 8χ 3χ
HV
DN2S
IC P5 Ch 6χCh 8χCh W 4 ASV5 DSV2 DS13 ANV3 χ C 5χbCh 6χv 5χbPC JY IC1 IC5 SIC1 CIC4 Oorb AZN4 AZV4 ASZ2 NELEM HMIN SSCH3 QV SSSSN SSBR NUMHBD HB1 TOTOP SHNHCX SSCL SHSOH HMAX STCH STSC SUMDELI SDO SSSO SSSH SAACH SAAS SDDC SDSN SDS SSSNH SHTVIN SUMI SSSS SHOTHER SHBINT3 SSF STN NHBINT2 SHCSATU SHVIN SSI SAAO KP3 EHOMO EHOMO-1 ELUMO µ 3 b
χ
C
5 b
used in the development of a second type of nonhierarchical model (Type II). In addition, TC-only, 3D-only, and QConly models were developed for comparison purposes. Two regression procedures from the SAS40 statistical software package were used to develop the models. When the number of independent variables was less than approximately 20-25, the all possible subset regression option was feasible. However, this option is very time intensive when dealing with a large number of independent variables; in which case, the stepwise regression option which optimizes the improvement of the explained variance (R 2) was used. In addition to constructing models based on the entire data set, the 469 chemicals were partitioned into a training set (N ) 351) and a test set (N ) 118), with an approximate 25/75 split. Models developed using the training set were then used to predict the vapor pressure of the chemicals in the test set. The partitioning was performed using the RANUNI function (a random number generator) of the SAS statistical package.40 3. RESULTS
3.1. Regression Analysis of the Complete Set of 469 Chemicals. The topostructural descriptors obtained through variable clustering were used in regression analysis, yielding the following five-parameter topostructural model. The inclusion of additional descriptors does not result in a significantly improved model. For example, even the best 12-parameter TS model explains only 49.8% of the variance with a standard error of 0.53.
an improved model. Including as many as 19 descriptors in the model results in an increase of only 0.2% in R 2 and no decrease in the standard error. Again repeating the regression, now adding the quantum chemical descriptors to those included in eq 2, we do find a model with slightly improved R 2 and F values. Nine of the descriptors from the previous model have been retained, and three have been replaced by quantum chemical descriptors.
log (pvap) ) 3.65 8χ + 0.61 3χbC - 2.79 AZV4 0.91 SHSOH + 0.14 SSCL + 0.46 SSF + 0.31 SSSO0.32 STN - 0.18 SHHBA - 0.14 EHOMO-1 0.09 ELUMO - 0.14 µ + 9.51 (3) n ) 496, R 2 ) 90.6%, s ) 0.23, F ) 364 In addition to performing hierarchical modeling, we developed models using each descriptor class independently in order to examine the performance of each class. The topochemical out-performed all other classes of descriptors, followed by the geometrical, the topostructural, and finally the quantum chemical, which produced a very poor model. Two nonhierarchical models were developed; the first of which (Type I) was obtained utilizing those TS and TC parameters selected by the independent variable clustering of each respective descriptor class as well as all geometrical and all quantum chemical descriptors (Table 3):
log (pvap) ) -0.64 6χ + 3.56 8χ + 0.73 6χc - 0.47 W 0.92 ANV5 + 4.03 (1)
log (pvap) ) - 2.59 0χv - 0.80 6χ + 0.86 P9 3.08 SIC0 - 2.11 ANV5 - 1.00 SHSOH - 0.34 STN + 0.20 SSSO + 0.21 SSF - 0.19 HB1 - 0.13 EHOMO-1 0.17 µ + 7.40 (4)
n ) 496, R 2 ) 48.7%, s ) 0.53, F ) 87.9
n ) 496, R 2 ) 91.3%, s ) 0.22, F ) 398
Regression analysis utilizing descriptors from the above topostructural model and those topochemical descriptors obtained through variable clustering results in a 12-parameter TS + TC model, with only one of the topostructural descriptors retained. There is a significant increase in the explained variance as well as a significant decrease in the standard error.
The second nonhierarchical model (Type II) was developed utilizing parameters selected by variable clustering of the entire set of 268 descriptors used in this study (Table 4):
log (pvap) ) 0.59 3χbC + 3.39 8χ - 2.70 AZV4 0.85 HMIN - 0.78 SHSOH + 0.26 SSCL + 0.56 SSF + 0.44 SSSO - 0.28 STN + 0.73 SAAO 0.25 SHCSATS - 0.28 SHHBA + 11.0 (2) n ) 496, R 2 ) 90.3%, s ) 0.23, F ) 354 When the geometrical descriptors are added to those in the TS + TC model and regression repeated, we do not find
log (pvap) ) 0.61 3χbc + 3.87 8χ - 2.81 AZV4 0.94 SHSOH + 0.26 SSSO - 0.38 STN + 0.32 SSF 0.13 HB1 - 0.19 µ - 0.15 EHOMO-1 - 0.08 ELUMO + 9.35 (5) n ) 496, R 2 ) 90.3%, s ) 0.23, F ) 388 It is interesting to note the similarity between the two nonhierarchically developed models (eqs 4 and 5), as well as the similarity between these models and the final hierarchical model given in eq 3. Although each of these models was derived using a different method, they each contain two connectivity indices, the same four E-state
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Table 5. Variable Clustering Results Using All 268 Descriptors and the Complete Set of 469 Diverse Compoundsa R 2 with own cluster
next closest
IWD hIWD W ID HD 0χ 1 χ P0 DN2S1 DN2S3 DN2S5 DN211 DN214
0.9954 0.9537 0.9985 0.9665 0.9515 0.9576 0.9720 0.9874 0.9638 0.9968 0.9675 0.9666 0.9786
0.8526 0.8964 0.8282 0.8821 0.9082 0.8465 0.8886 0.9030 0.7365 0.8154 0.7323 0.8406 0.9123
4
χPC 5χ PC 6χ PC
0.8064 0.9276 0.8316
HV IC DN2S2
R 2 with own cluster
next closest
AS11 AS12 AS14 AS15 DS11 DS14 DS15 ASN4 DSN4 DN2N2 DN2N3 DN2N4 ANS1
0.9265 0.8823 0.9854 0.9227 0.9355 0.9836 0.9046 0.9758 0.9673 0.9643 0.9683 0.9718 0.9911
0.5571 0.6291 0.5458
4 b
χ PC 5χb PC
0.9261 0.6972 0.9210
0.7521 0.4680 0.7384
DN213 DS13
0.9970 0.9983
IC0 IC1 SIC0 5χ
R 2 with own cluster
next closest
Cluster 1 0.7925 ANS2 0.8571 AN11 0.8762 AN13 0.7993 AN15 0.8547 ANN1 0.8502 ANN2 0.7970 ANN3 0.8588 ANN5 0.8512 ANV4 0χb 0.8219 1χb 0.9367 0.9138 AZV1 0.7833 AZV3
0.9622 0.8096 0.9902 0.9395 0.9867 0.9625 0.9894 0.9920 0.9712 0.9178 0.8944 0.9263 0.9385
0.7241 0.6803 0.8877 0.7170 0.8923 0.8823 0.8950 0.8788 0.9264 0.8190 0.8068 0.9230 0.9136
0.8437 0.9531
Cluster 2 6 b 0.5277 χ PC 4χv 0.5770 PC
0.8492 0.7810
ASV1 DSV1
0.8431 0.9188
Cluster 3 0.7371 ANV2 0.7510 IDCBAR
0.4954 0.5080
DSN1 DSN5
0.9698 0.9817
Cluster 4 0.5553 DN2N1 0.5149
0.8695 0.5056 0.9094
0.5622 0.4396 0.5620
SIC1 CIC0 CIC1
0.9427 0.8571 0.9318
6χ
0.8628 0.8326
0.5713 0.4912
P5 P6
SIC2 SIC3
0.8262 0.9503
0.4502 0.4860
ASZ1 ASZ2 ANZ1
0.9601 0.9761 0.7821
3χ Ch
0.9014
variable
R 2 with own cluster
next closest
AZS1 AZS2 AZN1 AZN2 AZN3 AZN5 IDC VW 3D WH 3DW KP0 KP1 KA1
0.9820 0.9660 0.9719 0.9570 0.9804 0.9590 0.9877 0.8813 0.8048 0.9934 0.7703 0.8260 0.7994
0.7904 0.7565 0.8518 0.8343 0.8693 0.8364 0.7906 0.7039 0.7523 0.8210 0.6782 0.6061 0.6081
0.4938 0.4675
5 v 6χv
PC
0.8848 0.8301
0.5229 0.4806
0.7456 0.9094
0.4718 0.7586
KP2 KA2
0.8774 0.8585
0.7028 0.7339
0.9975
0.4919
DN2N5
0.9968
0.4985
Cluster 5 0.4774 CIC2 0.6424 NELEM 0.6235 HMIN
0.7504 0.6896 0.2793
0.5960 0.5685 0.1171
SSCH3 QV
0.6198 0.6970
0.4079 0.6569
0.8720 0.8636
Cluster 6 5χb 0.6079 6χb 0.4437
0.8498 0.8346
0.5711 0.3437
5χv 6χv
0.7990 0.8207
0.5403 0.3331
SIC4 SIC5
0.9190 0.9142
Cluster 7 0.5810 CIC3 0.5872 CIC4
0.9198 0.9549
0.4286 0.3344
CIC5 SSSSN
0.9534 0.0250
0.3260 0.0141
0.6180 0.6299 0.2697
ANZ2 DSZ1
0.9621 0.8855
Cluster 8 0.4275 DSZ2 0.7642 DN2Z1
0.9341 0.9579
0.5766 0.7026
DN2Z2 SSBR
0.9097 0.3885
0.4748 0.0527
0.1369
4χ Ch
0.8785
Cluster 9 3χv 0.2030 Ch
0.8059
0.0884
4χv
Ch
0.8369
0.1538
0.7277
0.5997
HB1
0.6580
0.3809
variable
variable
variable
χ
PC
SHSNH2 SSNH2
0.7182 0.7145
0.0902 0.0677
NUMHBD
0.8165
Cluster 10 0.4173 SHHBD
M1 M2 2χ P1 P2
0.9876 0.9770 0.9322 0.9394 0.9876
0.8646 0.8394 0.7448 0.9323 0.7925
DN2S4 AS13 ASN1 ASN3 ASN5
0.9920 0.9330 0.9378 0.9738 0.9250
Cluster 11 0.8572 DSN3 0.7042 AN14 0.7103 ANN4 2χb 0.9237 0.7051
0.9875 0.9666 0.9759 0.8155
0.8606 0.9324 0.8281 0.6918
AZV2 TOTOP TETS2 PF
0.9580 0.6857 0.7302 0.9830
0.8049 0.6143 0.6607 0.7942
5χ C 6χ C
0.9257 0.8816
0.3132 0.2849
5χb
Cluster 12 5χv 0.3177 C 0.2860
0.7425
0.2871
6χv
0.6941
0.1294
6χb
0.9510 0.8774
P8
0.9826
0.3434
P9
0.7317
Cluster 13 8χ 0.1831
0.9910
0.3258
8χv
0.7443
0.3100
0.6372
Cluster 14 0.2053 NUMWHBD
0.9593
0.1721
SHWHBD
0.9590
0.1950
0.8373
0.3612
4χv
0.8234
0.1478
0.9767 0.9776
0.4277 0.4325
SI NCLASS
0.9500 0.9099
0.3881 0.4585
SHCHNX
0.9636
0.1916
C
C
SSCL
3χ C 4χ C
0.8900 0.9040
0.4731 0.2337
3χb 4χb
0.9193 0.9036
Cluster 15 3χv 0.4575 C 0.2299
O IORB Oorb
0.7798 0.9399 0.5996
0.4153 0.3578 0.3202
IC2 IC3
0.7441 0.9532
Cluster 16 0.5218 IC4 0.3922 IC5
C
C
C
C
698 J. Chem. Inf. Comput. Sci., Vol. 41, No. 3, 2001
BASAK
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Table 5 (Continued) R 2 with variable SHSOH SHTCH
own cluster
next closest
0.9328
0.2594
0.9404
0.0213
R 2 with variable HMAX STCH
R 2 with
own cluster
next closest
0.5149
R 2 with
own cluster
next closest
Cluster 17 0.2227 SSOH
0.9323
0.2313
0.9405
Cluster 18 0.0214 STSC
0.6613
0.0660
0.7570 0.8705
0.5451 0.5595
µ
0.8951
0.3689
variable
own cluster
next closest
0.5602
0.4499
6 v
0.8763
0.3917
EHOMO-1
0.5498
0.1764
SSSS
0.0959
0.0272
variable
SUMDELI GMAX
0.6720 0.8308
0.4506 0.4514
SDO SSSO
0.5226 0.3197
Cluster 19 0.1359 NUMHBA 0.0594 SHHBA
6
χCh NRINGS
0.9497 0.8542
0.3529 0.3672
NCIRC
0.8488
Cluster 20 6 b 0.3683 χ Ch
SHSSH
1.0000
0.0131
SSSH
1.0000
Cluster 21 0.0129
SAACH
0.9007
0.1528
SAAS
0.4891
Cluster 22 0.0907 SHAROM
0.8770
0.1530
0.8060
0.0216
0.5338
0.3821
0.9763
0.4082
0.9555 0.7834
0.6925 0.7401
SHOTHER
0.5780
0.5006
0.8587 0.8609 0.7634
0.7353 0.6109 0.6028
4χv AZV5 WT
0.7941 0.8775 0.9438
0.5111 0.7835 0.8706
SDDC
0.6835
0.0289
SDSN
0.6631
Cluster 23 0.0298 SDS
SHSSNH
0.9998
0.0563
SSSNH
0.9998
Cluster 24 0.0562
SDCH2
0.9983
0.1113
SHTVIN
0.9983
Cluster 25 0.1096
J JB
0.8335 0.9629
0.4565 0.3456
JX JY
0.9280 0.9685
Cluster 26 0.4131 SUMI 0.3495
5χ Ch
0.9748
0.4084
5χ b
0.9829
Cluster 27 5χv 0.3917 Ch
Ch
χ
C
DN212 DS12 DSN2
0.7763 0.8466 0.8833
0.7531 0.7536 0.7849
AN12 ASV2 ASV5
0.9131 0.9330 0.6139
Cluster 28 0.8918 DSV2 0.6714 ANV5 0.3636
3χ
P3
0.8863 0.8774 0.9302
0.7660 0.6275 0.7942
P4 ANV1 ANV3
0.8928 0.9428 0.9444
Cluster 29 3χb 0.6461 4χb 0.8426 3 v 0.9038 χ
NHBINT3
0.9968
0.1259
SHBINT3
0.9968
Cluster 30 0.1088
SSF
0.7701
0.1202
∆Hf
0.7701
Cluster 31 0.2161
P7
0.9466
0.3481
7χ
0.9610
Cluster 32 8χ 0.4520 Ch
0.1308
0.0296
7χv
0.8400
0.3162
0.4838 0.8401
0.3515 0.3607
STN
0.0614
0.0327
0.8758
0.4559
KA3
0.8684
0.3948
4χ
1χv
0.8822 0.8562
0.7630 0.6655
2χ v AZV4
0.8719 0.9029
Cluster 33 0.5619 AZN4 0.7507 FW
ASN2
0.8685
0.7028
PHIA
0.7772
Cluster 34 0.7160 KP3
0χv
NHBINT2
0.9999
0.2325
SHBINT2
0.9999
Cluster 35 0.2325
SHCSATS
0.7107
0.3141
ELUMO
0.8669
Cluster 36 0.3778 ELUMO+1
0.7256
0.4721
SHCSATU
0.6978
0.0793
SHVIN
0.6238
Cluster 37 0.0999 EHOMO
0.5703
0.2009
Cluster 38 SSI
1.0000
0.1167
SAAO
1.0000
0.0178
Cluster 39 a
Variables selected for regression analysis are indicated in bold type.
descriptors, one descriptor which encodes information about hydrogen bonding, the same 2-3 quantum chemical descriptors, and one triplet descriptor derived from the adjacency matrix and V (vertex degree) as the free term column vector.
These three models are also very similar with respect to statistical measures. A summary of all models developed on the full set of 469 compounds is given in Table 6. A scatter plot of the observed
QSPRS
FOR THE
ESTIMATION
OF
VAPOR PRESSURE
J. Chem. Inf. Comput. Sci., Vol. 41, No. 3, 2001 699
Table 6. Summary of Regression Results for the Complete Data Set Containing 469 Diverse Chemicals complete data set (N ) 469) descriptors
F
R2
s
χc, 6χ, 8χ, W, ANV5 3χb , 8χ, AZV , HMIN, SHSOH, SSCl, SSF, SSSO, STN, SAAO, 4 c SHCSATS, SHHBA, 3χb , 8χ, AZV , SHSOH, SSCl, SSF, SSSO, STN, SHHBA, E c 4 HOMO-1, ELUMO, µ 0 V 1 V χ , χ , SSF, SDO, SDSN, HMIN, SHSOH, STN, QV, NUMHBD 3DW, 3DW , V , KP , KA H W 1 2 ∆Hf, µ, ELUMO, EHOMO-1 0 V 6 χ , χ, P9, SIC0, ANV5, SHSOH, STN, SSSO, SSF, HB1, EHOMO-1, µ 3 b 8 χ c, χ, AZV4, SHSOH, STN, SSSO, SSF, HB1, EHOMO-1, µ, ELUMO
87.9 354
48.7 90.3
0.53 0.23
364
90.6
0.23
342 120 46.4 398 388
88.2 56.4 28.6 91.3 90.3
0.26 0.49 0.63 0.22 0.23
descriptor class 6
TS TS + TC TS + TC + QC TC 3D QC all classes (Type I) (nonhierarchical) all classes (Type II) (nonhierarchical)
Figure 1. Scatter plot of observed log (pVap)vs estimated log (pVap) using eq 4 for the set of 469 diverse compounds. Table 7. Summary of Regression Results for Training and Test Sets test set (N ) 118)
training set (N ) 351) descriptors
F
R2
s
R2
s
J, ANS1 3χb , 4χV, 8χ, AZV , TETS , SSF, SDO, SDSN, STN, SHHBD c 4 2 8χ, 3χb , AZV , SSF, SDSN, STN, SHHBD, E c 4 HOMO-1, ELUMO, µ 3χb , 4χV, AZV , TeTS , SSF, SDO, SDSN, STN, SHHBD c 4 2 3DW, 3DW , V , KA , KA H W 1 2 EHOMO, EHOMO-1, ∆Hf 3χb , 6χ , 8χ, 8χV, AZV , SSF, STN, NHBINT , SHHBD, c PC 4 2 EHOMO-1, ELUMO, µ 3χb , 8χ, AZV , SSF, STN, SSSSO, SHSOH, NHBINT 4 3 c EHOMO-1, ELUMO, µ,
111 228 250 234 88.3 54.7 250
48.9 87.0 88.0 86.1 56.1 32.1 89.9
0.53 0.27 0.26 0.28 0.49 0.61 0.24
39.1 85.9 84.8 85.9 54.0 11.7 81.0
0.58 0.28 0.29 0.28 0.50 0.78 0.32
300
90.7
0.23
85.4
0.29
descriptor class TS TS + TC TS + TC + QC TC 3D QC all classes (Type I) (nonhierarchical) all classes (Type II) (nonhierarchical)
8χ,
versus the estimated log (pvap) values using eq 4 is shown in Figure 1. 3.2. Regression Analysis of the Training and Test Sets. Summary statistics for all models developed on the training set and prediction results for the test set are provided in Table 7. A topostructural model consisting of three parameters explains 48.9% of the variance with a standard error of 0.53. The addition of topochemical descriptors improved the model significantly, increasing R 2 to 87.0% and decreasing s to 0.27. The improvement due to the addition of the topochemical descriptors is also evident in the test set statistics, with R 2 increasing from 39.1% to 85.9%, and s decreasing from 0.58 to 0.28. When the geometrical descriptors are added, we find again, as was the case in analysis of the complete
data set, an improved model is not obtained. The addition of quantum chemical descriptors yields a model showing only slight improvement with a slight decrease in the effectiveness of that model as evidenced by the test set results. The topochemical class independently produced a good model with good predictive ability. Neither the geometrical nor the quantum chemical descriptor classes produced acceptable models, with the quantum chemical model notably poor. As was done with the full data set, two nonhierarchical models were developed using the training set chemicals. Again, the first of these models (Type I) was derived using TS and TC parameters selected by independent variable clustering of the respective classes, in addition to all geometrical and all quantum chemical descriptors, and the
700 J. Chem. Inf. Comput. Sci., Vol. 41, No. 3, 2001
BASAK
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Table 8. QSPR Vapor Pressure Prediction Models model type
no. of parameters
N
R2
s
F
investigators
ref no.
CNN CNN CNN MLR MLR MLR MLR
8 10 7 7 5 10 12
65/420a 65/420a 52/352a 479 411 476 469
NRb NRb NRb 0.960 0.949 0.843 0.913
0.37 0.33 0.209 0.534 0.331 0.29 0.22
NRb NRb NRb NRb 1511.4 249.5 398
McClelland & Jurs (2000) McClelland & Jurs (2000) Goll & Jurs (1999) Liang & Gallagher (1998) Katritzky et al. (1998) Basak et al. (1997) Basak et al.
10 10 11 8 9 7 current study
a
Reported error is on external prediction set. Notation indicates: Nprediction set/Ntotal. bNR ) not reported.
second (Type II) was derived using parameters selected by variable clustering of the entire set of descriptors used in this study. While both methods resulted in acceptable models, the Type II model was the best overall training set model, with good predictive ability as indicated by the test set statistics. The Type I is very similar in terms of statistical measures; however, its predictive ability is slightly diminished as compared to that of the Type II model, the TC model, the TS + TC model, or the TS + TC + QC model. 4. DISCUSSION
The primary objective of the present study was to investigate the usefulness of an expanded set of theoretical molecular descriptors consisting of the major classes of topostructural as well as topochemical parameters in the prediction of vapor pressure. In an earlier study, Basak et al.7 used a set of 97 indices to predict VP for a set of 476 molecules. In this paper, we have used a group of 268 theoretical parameters in the development of QSPR models for a set of 469 diverse chemicals. We have developed QSPR models using our hierarchical approach as well as nonhierarchical methods (Tables 6 and 7). It was found that the hierarchical model and those developed from the full set of descriptors using nonhierarchical methods have similar predictive quality. It is interesting to note that topostructural and topochemical parameters explained most of the variance in the VP data, while the addition of geometrical and quantum chemical indices provided marginal improvement in model quality, at best. Our previous hierarchical QSAR/QSPR studies with various types of physicochemical, biomedicinal, and toxicological properties found the same pattern for different and diverse data sets. A few distinct features are evident when examining the best QSPR models given in Tables 6 and 7: (a) The majority of the models contain path connectivity or count of path length terms which encode information about paths of lengths six or greater. Such terms might represent information regarding the generalized shape and size of molecules which are important for intermolecular van der Waals type interaction. Another connectivity index, 3χbc, is present in the majority of the models. This index, a quantifier of molecular branching, also shows the importance of molecular shape in determining vapor pressure. (b) Each of the models has at least one parameter that characterizes hydrogen bonding. The coefficients of all hydrogen bonding terms are negative, indicating that the values of VP are inversely correlated with the strength of hydrogen bonding which determines the tendency of molecules to remain in the liquid state as
opposed to escaping to the gaseous phase. (c) Another group of parameters which have an important role in the VP QSPRs is the electropological indices. These indices collectively represent the various types of electronic interactions among molecules. It is of interest to compare the results of the current study with those of the major published studies in which VP QSPR models were developed utilizing large data sets (Table 8). The enhanced set of theoretical descriptors used in the current study led to improved models as compared to the earlier study by Basak et al.7 The data sets utilized by McClelland and Jurs,10 Liang and Gallagher,8 and Katritzky et al.9 are all structurally quite diverse. The best QSPR models in the current study are superior to the models reported by these investigators in terms of model error. It should be noted, however, that the results reported by the Jurs group10,11 are based on external prediction sets. Of the results reported in Table 8, only the model obtained by Goll and Jurs11 has a lower error than the best model developed in the current study; however, it must be noted that the data set they used was not as diverse, consisting strictly of hydrocarbons and halohydrocarbons, and the total number of compounds in their data set was approximately 25% less than the data set used by our group. The models developed in this study are based on easily calculable molecular descriptors which can be used in the routine estimation of vapor pressure of chemicals. ACKNOWLEDGMENT
This is contribution number 290 from the Center for Water and the Environment of the Natural Resources Research Institute. Research reported in this paper was supported by Grant F49620-98-1-0015 from the U.S. Air Force. The authors are thankful to Brian D. Gute and Gregory D. Grunwald for technical support. REFERENCES AND NOTES (1) (a) Mackay, D.; Shiu, W. Y.; Ma, K. C. In Illustrated Handbook of Physical-Chemical Properties and EnVironmental Fate for Organic Chemicals; Lewis Publishers: Boca Raton, FL, 1992; Vol. 1-4. (b) Lyman, W. J. In EnVironmental Exposure from Chemicals; Neely, W. B., Blau, G. E., Eds.; Chemical Rubber: Boca Raton, FL, 1985; Vol. I. (2) (a) Mackay, D. Finding Fugacity Feasible. EnViron. Sci. Technol. 1979, 13, 1218-1223. (b) Mackay, D.; Paterson,S. Calculating Fugacity. EnViron. Sci. Technol. 1981, 15, 1006-1014. (c) Mackay, D.; Paterson, S. Fugacity Revisited. EnViron. Sci. Technol. 1982, 16, 654A-660A. (3) Mackay, D.; Shiu, W. Y. A Critical Review of Henry’s Law Constants for Chemicals of Environmental Interest. J. Phys. Chem. Ref. Data 1981, 10, 1175-1199. (4) Reinhard, M.; Drefahl, A. Handbook for Estimating Physicochemical Properties of Organic Compounds; Wiley & Sons: New York, 1999.
QSPRS
FOR THE
ESTIMATION
OF
VAPOR PRESSURE
(5) Mackay, D.; Bobra, A.; Chan, D. W.; Shiu, W. Y. Vapor Pressure Correlation for Low-Volatility Environmental Chemicals. EnViron. Sci. Technol. 1982, 16, 645-649. (6) Banerjee, S.; Howard, P. H.; Lande, S. S. General Structure-Vapor Pressure Relationships for Organics. Chemosphere 1990, 21, 11731180. (7) Basak, S. C.; Gute, B. D.; Grunwald, G. D. Use of Topostructural, Topochemical, and Geometrical Parameters in the Prediction of Vapor Pressure: A Hierarchical QSAR Approach. J. Chem. Inf. Comput. Sci. 1997, 37, 651-655. (8) Liang, C.; Gallagher, D. A. QSPR Prediction of Vapor Pressure from Solely Theoretically-Derived Descriptors. J. Chem. Inf. Comput. Sci. 1998, 38, 321-324. (9) Katritzky, A. R.; Wang, Y.; Sild, S.; Tamm, T. QSPR Studies on Vapor Pressure, Aqueous Solubility, and the Prediction of Water-Air Partition Coefficients. J. Chem. Inf. Comput. Sci. 1998, 38, 720-725. (10) McClelland, H. E.; Jurs, P. C. Quantitative Structure-Property Relationships for the Prediction of Vapor Pressures of Organic Compounds from Molecular Structures. J. Chem. Inf. Comput. Sci. 2000, 40, 967-975. (11) Goll, E. S.; Jurs, P. C. Prediction of Vapor Pressures of Hydrocarbons and Halohydrocarbons from Molecular Structure with a Computational Neural Network Model. J. Chem. Inf. Comput. Sci. 1999, 39, 10811089. (12) Auer, C. M.; Nabholz, J. V.; Baetcke, K. P. Mode of Action and the Assessment of Chemical Hazards in the Presence of Limited Data: Use of Structure-Activity Relationships (SAR) Under TSCA, Section 5. EnViron. Health Perspect. 1990, 87, 183-197. (13) Basak, S. C.; Gute, B. D.; Grunwald, G. D. Relative Effectiveness of Topological, Geometrical, and Quantum Chemical Parameters in Estimating Mutagenicity of Chemicals. In QuantitatiVe StructureactiVity Relationships in EnVironmental Sciences VII.; Chen, F., Schuurmann, G., Eds.; SETAC Press: Pensacola, FL, 1998; Chapter 17, pp 245-261. (14) Basak, S. C.; Gute, B. D.; Grunwald, G. D. A Hierarchical Approach to the Development of QSAR Models Using Topological, Geometrical and Quantum Chemical Parameters. In Topological Indices and Related Descriptors in QSAR and QSPR; Devillers, J., Balaban, A. T., Eds.; Gordon and Breach Science Publishers: The Netherlands, 1999; pp 675-696. (15) Basak, S. C.; Gute, B. D.; Grunwald, G. D. Use of Topostructural, Topochemical and Geometric Parameters in the Prediction of Vapor Pressure: A Hierarchical QSAR Approach. J. Chem. Inf. Comput. Sci. 1997, 37, 651-655. (16) Basak, S. C.; Gute, B. D.; Grunwald, G. D. A Comparative Study of Topological and Geometrical Parameters in Estimating Normal Boiling Point and Octanol/Water Partition Coefficient. J. Chem. Inf. Comput. Sci. 1996, 36, 1054-1060. (17) Basak S. C.; Mills, D. R.; Balaban, A. T.; Gute, B. D. Prediction of Mutagenicity of Aromatic and Heteroaromatic Amines from Structure: A Hierarchical QSAR Approach. J. Chem. Inf. Comput. Sci. 2000, in press. (18) Gute, B. D.; Basak, S. C. Predicting Acute Toxicity of Benzene Derivatives Using Theoretical Molecular Descriptors: A Hierarchical QSAR Approach. SAR QSAR EnViron. Res. 1997, 7, 117-131. (19) Gute, B. D.; Grunwald, G. D.; Basak, S. C. Prediction of the Dermal Penetration of Polycyclic Aromatic Hydrocarbons (PAHs): A Hierarchical QSAR Approach. SAR QSAR EnViron. Res. 1999, 10, 1-15. (20) Basak, S. C.; Gute, B. D.; Grunwald, G. D. Assessment of Mutagenicity of Chemicals from Theoretical Structural Parameters: A Hierarchical Approach. SAR QSAR EnViron. Res. 1999, 10, 117-129. (21) Russom, C. L.; Anderson, E. B.; Greenwood, B. E.; Pilli, A. ASTER: An Integration of the AQUIRE Data Base and the QSAR System for Use in Ecological Risk Assessments. Sci. Total EnViron. 1991, 109/ 110, 667-670. (22) Basak, S. C.; Harriss, D. K.; Magnuson, V. R. POLLY 2.3; Copyright of the University of Minnesota, 1988. (23) Basak, S. C. H-Bond; Copyright of the University of Minnesota, 1988. (24) Wiener, N. Cybernetics; Wiley: New York, 1948.
J. Chem. Inf. Comput. Sci., Vol. 41, No. 3, 2001 701 (25) Randic´, M. On Characterization of Molecular Branching. J. Am. Chem. Soc. 1975, 97, 6609-6615. (26) (a) Kier, L. B.; Hall, L. H. Molecular ConnectiVity in Chemistry and Drug Research; Academic Press: New York, 1976. (b) Kier, L. B.; Hall, L. H. Molecular ConnectiVity in Structure-ActiVity Studies; Research Studies Press: Letchworth, 1986. (c) Kier, L. B.; Hall, L. H. Molecular Structure Description: The Electrotopological State; Academic Press: New York, 1999. (27) Bonchev, D.; Trinajstic´, N. Information Theory, Distance Matrix and Molecular Branching. J. Chem. Phys. 1977, 67, 4517-4533. (28) Roy, A. B.; Basak, S. C.; Harriss, D. K.; Magnuson, V. R. Neighborhood Complexities and Symmetry of Chemical Graphs and Their Biological Applications. In Mathematical Modelling in Science and Technology; 4th International Conference Zurich; Avula, X. J. R., Kalman, R. E., Liapis, A. I., Rodin, E. Y., Eds.; Pergamon Press: New York, 1983; pp 745-750. (29) (a) Basak, S. C. Use of Molecular Complexity Indices in Predictive Pharmacology and Toxicology: a QSAR Approach. Med. Sci. Res. 1987, 15, 605-609. (b) Ray, S. K.; Basak, S. C.; Raychaudhury, C.; Roy, A. B.; Ghosh, J. J. A Quantitative Structure Activity Relationship Study of Tumor Inhibitory Triazenes Using Bonding Information Content and Lipophilicity. ICRS Med. Sci. 1982, 10, 933-934. (c) Basak, S. C.; Magnuson, V. R. Molecular Topology and Narcosis. A Quantitative Structure-Activity Relationship (QSAR) Study of Alcohols Using Complementary Information Content (CIC). Arzneimitt.Forsch. Drug Res. 1983, 33, 501-503. (30) Basak, S. C.; Magnuson, V. R. Niemi, G. J.; Regal, R. R. Determining Structural Similarity of Chemicals Using Graph-Theoretic Indices. Discr. Appl. Math. 1988, 19, 17-44. (31) Balasubramanian, K.; Basak, S. C. Characterization of Isospectral Graphs Using Graph Invariants and Derived Orthogonal Parameters. J. Chem. Inf. Comput. Sci. 1998, 38, 367-373. (32) (a) Basak, S. C.; Grunwald, G. D. Use of Topological Space and Property Space in Selecting Structural Analogues. Math. Modelling Sci. Comput. In press. (b) Basak, S. C.; Gute, B. D.; Grunwald, G. D. Development and Applications of Molecular Similarity Methods Using Nonempirical Parameters. Math. Modelling Sci. Comput. In press. (c) Basak, S. C.; Gute, B. D.; Grunwald, G. D. Quantitative Comparison of Five Molecular Structure Spaces in Selecting Analogues of Chemicals. Math. Modelling Sci. Comput. In press. (33) Raychaudhury, C.; Ray, S. K.; Roy, A. B.; Ghosh, J. J.; Basak, S. C. Discrimination of Isomeric Structures Using Information Theoretic Indices. J. Comput. Chem. 1984, 5, 581-588. (34) (a) Balaban, A. T. Highly Discriminating Distance-Based Topological Index, Chem. Phys. Lett. 1982, 80, 399-404. (b) Balaban, A. T. Topological Indices Based on Topological Distances in Molecular Graphs. Pure Appl. Chem. 1983, 55, 199-206. (c) Balaban, A. T. Chemical Graphs. 48. Topological Index J for Heteroatom-Containing Molecules Taking into Account Periodicities of Element Properties. Math. Chem. (MATCH), 1986, 21, 115-122. (d) Balaban, A. T.; Filip, P. Computer Program for Topological Index J (Average Distance Sum Connectivity). Math. Chem. (MATCH) 1984, 16, 163-190. (35) Filip, P. A.; Balaban, T. S.; Balaban, A. T. A New Approach for Devising Local Graph Invariants: Derived Topological Indices with Low Degeneracy and Good Correlational Ability. J. Math. Chem. 1987, 1, 61-83. (36) Basak, S. C.; Balaban, A. T.; Grunwald, G. D.; Gute, B. D. Topological Indices: Their Nature and Mutual Relatedness. J. Chem. Inf. Comput. Sci. 2000, 40, 891-898. (37) (a) MOLCONN-Z; Hall Associates Consulting: Quincy, MA. (b) Hall, L. H.; Kier, M. B. Molecular Structure Description: The Electrotopological State; Academic Press: New York, 1999. (38) Tripos Associates, Inc.: St. Louis, MO, 1994. (39) Stewart J. J. P. MOPAC Version 6.00; QCPE #455; Frank J. Seiler Research Laboratory: U.S. Air Force Academy, CO, 1990. (40) SAS/STAT. User’s Guide, Release 6.03 ed.; SAS Institute: Cary, NC, 1988.
CI000165R
